At what volume of the gym is the number of molecules in the air inside the gym 100 times greater than

At what volume of the gym is the number of molecules in the air inside the gym 100 times greater than the number of atoms in an iron bar weighing 100 kg? Assume that the air is under normal conditions.

Given: N1 (number of air molecules in the gym) = 100N2 (number of atoms in an iron bar); m2 (rod weight) = 100 kg.

Constants: ρ (air density at standard conditions) = 1.292 kg / m3; M1 (molar mass of air) = 28.98 g / mol; M2 (molar mass of iron) = 55.845 g / mol.

To determine the volume of the sports hall, we use the equality (m / M = N / Na): N2 * M2 / m2 = Na = N1 * M1 / m1 = N1 * M1 / (ρ * V) and V = N1 * M1 * m2 / ( ρ * N2 * M2).

Calculation: V = 100 * 28.98 * 100 / (1.292 * 1 * 55.845) = 4016.5 m3.